Решение задачи N4010 теория вероятностей Байеса

4010. The shop receives the same type of products from three plants, with the 1st plant supplying 40% of the products, the 2nd plant - 20%, the 3rd plant - 40%. Among the products of the 1st plant, 90% are top-notch, among the products of the 2nd - 90%, of the 3rd - 80%. Bought one product. It turned out to be first-rate. Determine the probability that the purchased product is produced by the 1st plant.

Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)